the point (-3,r) and (2,-3) lie on a line with the slope -3. find the missing coordinate r.

Answer 1

(1) slope intercept form y = mx + b

(2) given slope of -3 gives y = -3x + b but we don't yet know b

(3) point on this line (2, -3) gives -3 = -3(2) + b => b = 3 and required line y = -3x + 3

(4) point on this line (-3, r) gives r = -3(-3) + 3 => r = 9 + 3 = 12 or (-3,12)

OR

(1) gradient of line, m = change in y / change in x = (y2 - y1) / (x2 - x1)

(2) gradient is given -3

(3) two points given (2, -3) and (-3, r)

(4) hence -3 = (r - -3) / (-3 - 2) => (-3)(-5) = r + 3 => r = 12 and point is (-3, 12)